Multi-qubit time-varying quantum channels for NISQ-era superconducting quantum processors

Abstract

Recent experimental studies have shown that the relaxation time ($T_1$) and the dephasing time ($T_2$) of superconducting qubits fluctuate considerably over time. To appropriately consider this time-varying nature of the $T_1$ and $T_2$ parameters, a new class of quantum channels, known as Time-Varying Quantum Channels (TVQCs), has been proposed. In previous works, realizations of multi-qubit TVQCs have been assumed to be equal for all the qubits of an error correction block, implying that the random variables that describe the fluctuations of $T_1$ and $T_2$ are block-to-block uncorrelated, but qubit-wise perfectly correlated for the same block. Physically, the fluctuations of these decoherence parameters are explained by the incoherent coupling of the qubits with unstable near-resonant two-level-systems (TLS), which indicates that such variations may be local to each of the qubits of the system. In this article, we perform a correlation analysis of the fluctuations of the relaxation times of multi-qubit quantum processors ibmq\_quito, ibmq\_belem, ibmq\_lima, ibmq\_santiago and ibmq\_bogota. Our results show that it is reasonable to assume that the fluctuations of the relaxation and dephasing times of superconducting qubits are local to each of the qubits of the system. Based on these results, we discuss the multi-qubit TVQCs when the fluctuations of the decoherence parameters for an error correction block are qubit-wise uncorrelated (as well as from block-to-block), a scenario we have named the Fast Time-Varying Quantum Channel (FTVQC). Furthermore, we lower bound the quantum capacity of general FTVQCs based on a quantity we refer to as the ergodic quantum capacity. Finally, we use numerical simulations to study the performance of quantum error correction codes (QECC) when they operate over FTVQCs.

21 pages

References in corpus (7)

• Surface codes: Towards practical large-scale quantum computation
• Decoherence benchmarking of superconducting qubits
• A Survey on Quantum Channel Capacities
• Degenerate Quantum Codes for Pauli Channels
• Computing the distance between quantum channels: Usefulness of the Fano representation
• Coherent superconducting qubits from a subtractive junction fabrication process
• Performance of surface codes in realistic quantum hardware

Cited by in corpus (6)

• Decoding algorithms for surface codes
• Performance enhancement of surface codes via recursive MWPM decoding
• Detection of temporal fluctuation in superconducting qubits for quantum error mitigation
• The superadditivity effects of quantum capacity decrease with the dimension for qudit depolarizing channels
• Magnetic Field Detection Using a Two-Qubit System Under Noisy Heisenberg Interaction
• Error Mitigation of BQP Computations using Measurement-Based Verification